Ireland and France are also bidding to host the tournament
South Africa has re-entered the race to host the Rugby World Cup in 2023.
The South African government has lifted a ban on bidding for international rugby events after improvements in racial diversity in the sport.
Ireland and France are also vying to host the tournament with World Rugby set to make their final decision later this year.
"This is great news and a tribute to the work that the sport has been doing in recent years to stay in tune and relevant to modern South Africa," said SA Rugby president Mark Alexander.
"We can now put the finishing touches to what we believe will be an outstanding bid to host the 2023 Rugby World Cup.
"We have kept the ministry up to speed with our thinking and state of preparation throughout the suspension and continue to enjoy an excellent relationship with our sports leaders."
The South African Minister for Sport and Recreation Thulas Nxesi spoke of off the field progress made in rugby which has paved the way for
"I would like to congratulate rugby, cricket and netball on their improved scores, you were clearly willing to walk the extra mile," he said.
"Their right to bid for and host major sporting events, which was revoked before, is hereby immediately reinstated.
"But we would like to re-emphasise our expectations for sporting federations to take charge and provide leadership at school and club levels."
Ireland, France and South Africa will discover the fate of their bid in November.